Automata Theory Part B

A conceptual illustration of Automata Theory, featuring abstract representations of languages, machines, and logical proofs, with an academic atmosphere.

Exploring Automata Theory

Test your understanding of Automata Theory with this comprehensive quiz designed for students and enthusiasts alike. With 30 challenging questions, you will gain insights into logical proofs, theorems, and important concepts within the realm of formal languages and computations.

This quiz covers a variety of topics including:

Pumping Lemma
Proof Techniques
Logical Equivalences
Properties of Integers

30 Questions8 MinutesCreated by LogicalProof435

Let the statement be “If n is not an odd integer then the square of n is not odd.”, then if P(n) is “n is a not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof, we should prove _________

�nP ((n) → Q(n))

�n~(P ((n)) → Q(n))

�nP ((n) → ~(Q(n)))

� nP ((n) → Q(n))

While applying Pumping lemma over a language, we consider a string w that belong to L and fragment it into _______ parts.

Which of the arguments is invalid in proving that the sum of two odd numbers is not odd?

3 + 3 = 6, hence true for all

All of the mentioned

2n +1 + 2m +1 = 2(n+m+1) hence true for all

None of the mentioned

______ is used as a proof for irregularity of a language

Pumping lemma

Conjecture

Corollary

None of the mentioned

A proof that p → q is true based on the fact that q is true, such proofs are known as ____

Trivial proof

Direct proof

Contrapositive proofs

Proof by cases

A proof that p → q is true based on the fact that q is true, such proofs are known as _____

Trivial proof

Direct proof

Proof by cases

Contrapositive proofs

In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?

Direct proof

Proof by Contradiction

Vacuous proof

Mathematical Induction

In pumping lemma, If we select a string w such that w∈L, and w=xyz. Which of the following portions cannot be an empty string?

all of the mentioned

Let the statement be “If n is not an odd integer then square of n is not odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove ___

�nP ((n) → Q(n))

�n~(P ((n)) → Q(n))

� nP ((n) → Q(n))

�nP ((n) → ~(Q(n)))

A proof that p → q is true based on the fact that q is true, such proofs are known as …...

Direct proof

Trivial proof

Contrapositive proofs

Proof by cases

When to proof P→Q true, we proof P false, that type of proof is known as:

Direct proof

Contrapositive proofs

Mathematical Induction

Vacuous proof

To prove a statement p is true, you may assume that it is false, and then proceed to show that such an assumption leads a contradiction with a known result. This is called:

Direct proof

Trivial proof

Proof by contradiction

Proof by Induction

Let the statement be “If n is not an odd integer then sum of n with some not odd number will not be odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “sum of n with some not odd number will not be odd.” A proof by contraposition will be

�nP ((n) → Q(n))

� nP ((n) → Q(n))

�n~(P ((n)) → Q(n))

∀n(~Q ((n)) → ~(P(n)))

A theorem used to prove other theorem is known as

Lemma

Conjecture

Corollary

None of the mentioned

For m = 1, 2, …, 4m+2 is a multiple of is known as….:

Lemma

Corollary

None of the mentioned

Conjecture

All of the following statements could be proven with a direct proof EXCEPT: Let P: This is a great website, Q: You should not come back here. Then ‘This is a great website and you should come back here.’ is best represented by….:

~P V ~Q

P ∧ ~Q

P V Q

P ∧ Q

A proof that p → q is true based on the fact that q is true, such proofs are known as….:

Direct proof

Trivial proof

Contrapositive proofs

Proof by cases

The statement, “At least one of your friends is perfect”. Let P (x) be “x is perfect” and let F (x) be “x is your friend” and let the domain be all people….:

�x (F (x) → P (x))

�x (F (x) ∧ P (x))

�x (F (x) → P (x))

A theorem used to prove other theorems is known as ….:

Lemma

Conjecture

Corollary

None of the mentioned

(p →q) ∧ (p →r) is logically equivalent to

p→(q ∨ r)

p→(q ∧ r )

p ∧ (q→r)

P ∧ (q→r)

In proving π as irrational, we begin with assumption √7 is rational in which type of proof?

Direct proof

Proof by Contradiction

Trivial proof

�nP ((n) → Q(n))

� nP ((n) → Q(n))

�n~(P ((n)) → Q(n))

�n(P ((n)) → Q(n))

A proof that p → q is true based on the fact that q is true, such proofs are known as

Direct proof

Proof by Contradiction

Trivial proof

Vacuous proof

(p → r) ∨ (q → r) is logically equivalent to

(p ∧ q) ∨ r

(p ∧ q) → r

(p ∨ q) → r

(p → q) → r

In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?

Proof

Direct proof

Proof by Contradiction

Mathematical Induction

A proof that p → q is true based on the fact that q is true, such proofs are known as

Direct proof

Trivial proof

Proof by cases

Contrapositive proofs

A theorem used to prove other theorems is known as

Lemma

Conjecture

Corollary

None of the mentioned

�nP ((n) → Q(n))

�n~(P ((n)) → Q(n))

� nP ((n) → Q(n))

�nP ((n) → ~(Q(n)))

∀nP ((n) → Q(n))

�n~(P ((n)) → Q(n))

� nP ((n) → Q(n))

�n(~Q ((n)) → ~(P(n)))

A proof that p → q is true based on the fact that q is true, such proofs are known as:

Direct proof

Trivial proof

Contrapositive proofs

Proof by cases

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